Autocorrelation
Masatoshi Katabuchi
2020/11/2 (updated: 2020-11-01)
Materials for the AFEC-X 2020::XTBG. An introduction for modeling autocorrelaition using R.
Objectives
- A quick review for likelihood methods
- Understanding what autocorrelation is
- Getting an idea for handling autocorrelation
Course materials for 2020-11-2 AFEC at XTBG.
Prerequisites
install.packages("spdep")library(tidyverse)
library(spdep)Spatial autocorrelaiton
- Neighbors affect the observation.
2D
Let’s condier maps with some enviromental variables (e.g., soil N, soil moisture…).
Soil N (z0) can be uniformly distributed.
Soil N (z) can show aggreated patterns.
ggplot(dat, aes(x = x, y = y, fill = hab)) +
geom_raster()
dat2 <- dat %>%
# mutate(hab_dummy = ifelse(hab == "valley", 0, 1)) %>%
mutate(trait = rnorm(nrow(.), mu, 0.3)) # based on z
dat2 %>%
ggplot(., aes(x = hab, y = trait, col = hab)) +
geom_violin() +
geom_jitter(width = 0.2)
- Ridge sites have greater trait values (e.g., thick dense leaves to grow well in dry conditions)
- Is this because those traits are favored in ridge sites?
- Is this just because neighbors have similar trait values (spatial autocorrelation)?
\[ Y = X \beta + \rho W (Y - X \beta) + \epsilon \]
def
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What is autocorrelation?
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Simple correlation
One dimensional autocorrelation
Two dimensional autocorrelation
Likelihood methods
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